an identification of better engineering college with ... · the technique for order preference by...

I.J. Modern Education and Computer Science, 2016, 5, 19-31 Published Online May 2016 in MECS (http://www.mecs-press.org/)

DOI: 10.5815/ijmecs.2016.05.03

Copyright © 2016 MECS I.J. Modern Education and Computer Science, 2016, 5, 19-31

An Identification of Better Engineering College

with Conflicting Criteria using Adaptive TOPSIS

T. Miranda Lakshmi Research Scholar, Research and Development Centre, Bharathiyar University, Coimbatore, India.

Email: [email protected]

V. Prasanna Venkatesan Associate Prof., Department of Banking Technology, Pondicherry University, Puducherry, India.

Email: [email protected]

A. Martin Associate Professor, Department of MCA, Sri Manakula Vinayagar Engg. College, Puducherry, India.

Email: [email protected], [email protected]

Abstract—Students like to find better engineering college

for their higher education. It is very challenging to find

the better engineering college with conflicting criteria. In

this research, the criterion such as academic reputation

and achievements, infrastructure, fees structure, location,

quality of the faculty, research facilities and other

criterion are considered to find the better engineering

college. Multi Criteria Decision Making (MCDM) is the

most well known branch of decision making under the

presence of conflicting criteria. TOPSIS is one of the

MCDM technique widely applied to solve the problems

which involves many number of criteria. In this research,

TOPSIS is Adaptive and applied to find better

engineering college. To evaluate the proposed

methodology the parameters such as time complexity,

space complexity, sensitivity analysis and rank reversal

are considered. In this comparative analysis, better

results are obtained for Adaptive TOPSIS compared to

COPRAS.

Index Terms—Multi Criteria Decision Making (MCDM)

evaluation, TOPSIS, Adaptive TOPSIS, better

engineering college, COPRAS, Rank reversal, repeated

ranking.

I. INTRODUCTION

Decision making becomes an integral part in our daily

lives and will be used for complex problems including

problems with multiple conflicting criteria. Multi-criteria

decision making (MCDM) is a well-known decision

making process based on the progression of using

methods and procedures of multiple conflicting criteria

into the planning process. In other words, MCDM refers

to making decision in the presence of multiple, numerous

and usually that involve conflicting numbers of criteria.

MCDM provides a step by step procedure for which a

consensus decision can be made by a group of decision

makers. This well-defined procedure can reduce the

amount of arguments or conflicts involved. MCDM plays

an important role in solving complex problems. The

development of MCDM discipline is closely related to the

advancement of computing technology. With this

development, it is possible to conduct systematic analysis

of complex MCDM problems. Furthermore, the extensive

use of computing software has generated a huge amount

of information, which makes MCDM increasingly

important and useful in supporting decision making.

Multi-criteria decision making aims at selecting the

"best" alternative from a set of alternatives which satisfy

all the criteria. In order to select the best alternative many

MCDM techniques are used and applied in various

applications. In this research, most widely used MCDM

technique, TOPSIS is Adaptive and compared with

COPRAS method. To evaluate the proposed work,

Adaptive TOPSIS and COPRAS method is likely to be

applied in ranking the engineering colleges.

The rest of the paper is set out as follows. In section 2,

the relative literature are reviewed, section 3 describes

research approach and design, section 4 describes the

proposed methodology , section 5 describes the

experimental design, section 6 presents the result and

discussion, and finally ended up with the conclusion, the

findings of the study and the future research.

II. PRIOR RESEARCH

“Decision making is the study of identifying and

choosing alternatives based on the values and Preferences

of the decision maker. Making a decision implies that

there are alternative choices to be considered, and in such

a case it not only used to identify as many of these

alternatives as possible but to choose the one that best fits

with our goals, objectives, desires, values, and so on”[1]

Zeleny (1982) opens his book “Multiple Criteria

Decision Making” with a statement, “It has become more

and more difficult to see the world around us in a one-

dimensional way and to use only a single criterion when

judging what we see”. Multi-criteria decision making

(MCDM) aims at selecting the "best" alternative from a

20 An Identification of Better Engineering College with Conflicting Criteria using Adaptive TOPSIS


set of alternatives which have to satisfy multiple

objectives characterized by different criteria.

MCDM also referred as:

1. Multi-Criteria Decision Analysis (MCDA).

2. Multi-Dimensions Decision Making (MDDM).

3. Multi-Objective Decision Making (MODM).

4. Multi-Attributes Decision Making (MADM).

Alternatives: Alternatives represent the different

choices of action or entities available to the decision

maker. Usually, the set of alternatives is assumed to be

finite, ranging from several to hundreds.

Criteria: Criteria represent the different dimensions

from which alternatives can be viewed

Fig.1. Multi Criteria Decision Making Process

A. TOPSIS

The Technique for Order Preference by Similarity to

Idea Solution (TOPSIS) was first developed by Hwang

and Yoon in 1981. It is relatively easy and fast, and it is

most widely used method with a systematic procedure.

This method is based on notation that the chosen

alternative should have the shortest Euclidean distance

from the ideal solution [2]. The positive-ideal solution is a

solution that maximizes the benefit criteria and minimizes

the cost criteria, whereas the negative ideal solution

maximizes the cost criteria and minimizes the benefit

criteria. Many researchers have made the comparative

study of TOPSIS method with other Re345method in

specific domain because of its simplicity and easiness to

use. The First Step of TOPSIS Method is Normalization.

Normalization has been used to deal with incongruous

criteria dimension. Some of the normalization methods

for TOPSIS is mention by [3]. Two methods for

normalizing ratings are introduced, Gaussian

normalization method and Decoupling normalization

method by (Jin and Si, 2004).

Chen and Hwang, 1992 transformed Hwang and Yoon,

1981’s method into a fuzzy case. This fuzzy TOPSIS

method offered a fuzzy relative closeness for each

alternative, and the closeness was badly distorted and

over exaggerated because of the reason of fuzzy

arithmetic operations. Ref. [5] have proposed

methodology consists of 3 stages: Identification of the

criteria to be used in the model, FAHP computation and

Ranking the alternative using VIKOR, TOPSIS,

ELECTRE and PROMETHEE. The Weight of the criteria

is computed using FAHP method. This paper compares

the four methods to choose the best alternative among the

various popes material in Sugar industry. The Result of

VIKOR Method is compared with TOPSIS, ELECTRE

and PROMETHEE.

Ref. [6] compares AHP and TOPSIS method using

Fuzzy approach for supplier selection process. Fuzzy

AHP is more appropriate than the Fuzzy TOPSIS when

the purpose is to replace the supplier. Ref. [7] proposed a

new approach AHP and GA method with TOPSIS to

determine the quality value of cotton fiber in the textile

industry. The Result of GA – TOPSIS approach was

found to be the best method. [8] present a comparison of

VIKOR and TOPSIS methods, which are based on

distance measures. The focus of the comparison is on the

properties of the aggregating function as well as on the

normalization. Ref. [9] has compared six methods

Weighted Sum Method (WSM), Weighted Product

Method (WPM), VIKOR, PROMETHEE and TOPSIS for

building design selection problem. Additionally, a method

PEG – Theorem is employed. This method is a bit

different from other method and it doesn’t require any

preference information form the decision maker [20], [21].

Ref. [10] has taken five material selection problems.

These problems are solved using common MCDM

method namely, VIKOR, TOPSIS, ELECTRE. It is found

that among the three, VIKOR method is best in ranking

performance. Ref. [11] made a comparison on ELECTRE,

TOPSIS, PROMETHEE and VIKOR method for the

seismic retrofit decision problem. The comparison is

made based on the ease of applicability, reliability and

robustness of the choice, degree of decision maker’s

influence on the results. Table 2.1 describes the

Techniques combined and compared with TOPSIS [12].

Working Procedure of TOPSIS

Step 1: Construct normalized decision matrix by using

the vector normalization method.

√∑

(1)

Where, is the original rating of the decision matrix

and is the normalized value of the decision matrix.

Step 2: Construct the weighted normalized decision

matrix by assigning different value (weight) to each

criteria.

(2)

Where the weight for j is is the criterion.

Step 3: Determine the Positive Ideal Solution (PIS) &

Negative Ideal Solution (NIS).

An Identification of Better Engineering College with Conflicting Criteria using Adaptive TOPSIS 21


, (3)

Where

( ) if j⋲ ; ( ) if j⋲ }

, (4)

Where

( ) if j⋲ ; ( ) if j⋲ }

Step 4: Calculate the Distance of each alternative by

applying the Euclidean Distance method.

The distance from Positive Ideal Solution is:

√∑(

)

(5)

Similarly, the distance from Negative Ideal Solution is:

√∑

(6)

Step 5: Calculate the relative closeness to the ideal

solution .

(7)

Step 6: Rank the alternatives by selecting the

alternative with closest to 1.

B. COPRAS

In 1996, Zavadskas and Kaklauskas created this

method. It is used for evaluation of minimizing and

maximizing criteria. A single criterion cannot give a full

shape of the goal pursed by various clients. The COmplex

PRoportional ASsessment (COPRAS) method is

prioritizing the alternative on the basics of several criteria

along with associated criteria weights. Ref. [13] uses a

step wise ranking and evaluating procedure of the

alternative in terms of significance and utility degree. The

degree of utility for each alternative is shown as a

percentage from 0 to 100 %. The percentage shows

whether the alternative is worst or best than the other

existing alternatives [14]. Ref. [13] said problems with

multiple attributes are often too large for a decision maker

to comprehend in their entirety.

In 1982, Deng developed the Grey System theory and

in 1988. Deng presented a Grey Decision support system.

Later in 2008, Zavadskas developed the COPRA – G

method. Since the Grey Relational analysis is used in

COPRAS method it is easy to calculate the discrete and

imprecise data. [16] made a comparative analysis on

SAW and COPRAS method. The economic developments

in 2003 of four countries are examined. Ref. [17] has

compared AHP, TOPSIS and COPRAS for IPL Bowlers

performance in IPL. Each method used for specific

performance measure. to calculate the weight between

criterion AHP method is used. The performance

evaluation of Fast-Bowlers & Spinner in three IPL is

evaluated by TOPSIS method. The overall performance

of bowlers is evaluated by COPRAS method. Ref. [13]

applied COPRAS-G method to the selection of the

effective walls for dwelling house. Ref. [10] made a

comparative study on two almost unrevealed multi-

criteria approaches, namely complex proportional

assessment (COPRAS) and additive ratio assessment

(ARAS) - based methods for solving a gear material

selection problem in manufacturing industry.

Table 1. Comparison of Characteristic between TOPSIS and COPRAS

S. No

Characteristic TOPSIS COPRAS

1 Category MADM MADM

2 Core process

Positive Ideal

Solution and Negative Ideal

Solution

Minimization

Index and Maximization

Index

3 Attribute Given Given

4 Normalization

technique used

Vector

normalization

Vector

normalization

5 Weight Elicitation

Given Given

6 No of

alternative and attributes

Many more Many more

7 Ranking

Ranking based

on Relative

Closeness Coefficient

Ranking based on Utility

Degree

Working Procedure for COPRAS

The COPRAS method [15] uses a stepwise ranking and

evaluating procedure of the alternatives in terms of

significance and utility degree. The procedure of the

COPRAS method consists of the following steps:

Step 1: Selecting the set of the most important

attributes, describes the alternative.

Step 2: Construct the Decision Matrix

(1)

Where stands for the number of alternatives,

stands for the number of the attributes.

Step 3: Determining the weight of the attributes



Step 4: Normalization of the Decision Making Matrix

by

∑

(2)

Where in the th

alternative of a solution; m

is the number of attributes; n is the number of the

alternatives compared. Normalized decision-making

matrix

(3)

Step 5: Calculation of the Weighted Normalized

Decision Matrix .

.

(4)

Weighted Normalized decision-making matrix:

(5)

Step 6: Calculate maximization index of the alternative.

∑ (6)

Step 7: Calculate minimization index of the alternative.

∑ (7)

Step 8: Calculation of the relative weight of each

alternative .

∑

∑

(8)

Step 9: Calculation of the utility degree of each

alternative.

(9)

Where and are the significance of projects

obtained from Eq. (8).

C. Findings of the Survey

MCDM has many methods which capture much

attention from researchers in evaluating, accessing and

ranking the alternatives in different applications.

Numerous MCDM methods are developed to solve the

real – world decision problems. TOPSIS method is

widely used which work to satisfactorily across different

application area. Since many applications are evaluated

using TOPSIS method. This method is not applied in

evaluating the college selection process. From the survey

it also found that only limited work made a comparative

study on TOPSIS method with COPRAS method.

It is possible to combine (hybrid) TOPSIS with

other kinds of MCDM method. From the literature

review very limited work has been found to

simplify the TOPSIS.

Since there are many normalization techniques,

only vector normalization is used in TOPSIS

method.

From the literature it is found that TOPSIS steps

have not been Adaptive.

Sensitivity analysis is the parameter which is most

widely used in evaluating the efficiency of the

MCDM method.

In order to make the steps easy the generalized TOPSIS

steps are compressed. On simplifying this TOPSIS

method it will obtain a lesser amount of time and space

complexity. To find the efficiency of the proposed work,

COPRAS method is compared with Adaptive TOPSIS.

The evaluation parameters, Sensitivity analysis and

ranking reversal are performed where it has found that

Adaptive TOPSIS is more efficient than COPRAS

method.

III. RESEARCH APPROACH AND DESIGN

MCDM is used to evaluate different optimal and

feasible criteria to choose the best alternative. It contains

many methodology among those TOPSIS is one of the

well known and the most acceptable methodology. The

Adaptive- TOPSIS methodology is introduced in the

proposed work to improve the ranking efficiency of the

algorithm in an efficient manner. There are many

normalization techniques where TOPSIS contains only

vector normalization. In Adaptive TOPSIS the

normalization is change into linear sum based

normalization. To evaluate the proposed approach it is

applied in the ranking the engineering college. The

decision matrix is formulated for ranking. The formulated

matrix is applied in the Adaptive TOPSIS and COPRAS

method. This Adaptive – TOPSIS method is compared

with COPRAS method, in the direction of finding the

better MCDM Method. The best MCDM Method among

Adaptive TOPSIS and COPRAS is evaluated based on

the performance of these methodologies Time

Complexity (Big O) and Space Complexity, Sensitivity

Analysis and Ranking Reversal. When comparing these

algorithms, the proposed approach attains better

performance.



IV. PROPOSED METHODOLOGY

TOPSIS is most widely used method among many

MCDM techniques. TOPSIS was developed by Hwang

and Yoon in 1981. In Generalized TOPSIS method, there

is an individual step for every process. In the proposed

work, the TOPSIS method is Adaptive. In general,

TOPSIS method uses vector normalization to normalize

the decision matrix, whereas the Adaptive TOPSIS

methodology uses Gaussian normalization to normalize

the raw values of the decision matrix [4]. Similarly, the

stepwise procedure for generalized TOPSIS method is

Adaptive in order to make the process easy.

A. Working Procedure for Adaptive –TOPSIS

Step 1: Construct normalized decision matrix by using

the linear sum based normalization method.

√∑

(1)

Where stands for the rating for criteria j

Step 2: Calculate the Distance of each alternative by

applying the Euclidean Distance method. The distance

from Positive Ideal Solution is:

√∑ (( ) ( ))

(2)

Similarly, the distance from Negative Ideal Solution is:

√∑ (( ) ( ))

(3)

Step 3: Calculate the relative closeness to the ideal

solution .

(4)

Step 4: Ranking the alternatives by selecting the

alternative with closest to 1

V. EXPERIMENTAL DESIGN

A. Dataset Collection

There are wide ranges of colleges and they offer many

course. But most of the student prefers to go to

engineering, making a decision about the correct

engineering college to choose from many options that are

available. The question then arises of how to decide a

college when there are thousands of engineering colleges

in India. For selecting the best engineering college student

may look for different criteria’s. Based on those criteria

they will select the best college and course. The data is

collected from post graduate student about the 17

engineering in Cuddalore and Puducherry. 14 criteria are

taken for evaluating the college. The average data are

calculated to formulate the decision matrix. Table 2 shows

original matrix.

Table 2. Original Decision Matrix

C

1

C

2

C

3

C

4

C

5

C

6

C

7

C

8

C

9

C

1

0

C

1

1

C

1

2

C

1

3

C

1

4

A

1 4 3 3 2 3 3 3 3 3 3 3 2 4 3

A

2 4 4 3 3 3 3 3 4 3 3 3 3 3 3

A

3 3 2 3 3 3 3 3 2 3 2 3 3 2 3

A

4 3 3 3 3 3 3 2 3 3 3 3 3 3 3

A

5 3 2 3 3 3 3 2 3 3 2 3 3 3 3

A

6 4 4 3 3 4 3 4 3 3 4 3 4 2 3

A

7 4 5 4 4 4 4 3 4 4 4 4 3 4 4

A

8 4 5 5 4 5 4 4 4 4 4 4 5 4 4

A

9 4 4 4 3 4 3 3 4 4 3 3 4 4 3

A

1

0

3 3 3 3 3 3 3 2 2 3 3 3 3 3

A

1

1

3 3 3 2 3 3 3 3 2 3 2 3 3 3

A

1

2

2 3 3 3 2 3 3 3 3 3 3 3 3 3

A1

3

3 3 3 3 3 3 3 3 3 3 3 3 3 3

A

1

4 4 3 3 3 3 3 3 3 2 3 3 3 4 3

A

1

5

3 3 3 3 3 3 3 2 3 3 3 3 1 3

A

1

6

3 3 3 3 2 3 2 3 1 3 3 3 2 3

A

1

7

4 4 4 3 3 4 3 4 4 4 4 4 4 3

The weights for the criteria play an important role

where it normalizes the decision matrix. Table 3 shows

the weights for the criteria.



Table 3. Weights for Criteria

Criteria Weight

( )

Academic Reputation/ Ranking of the College

0.7735

Academic Achievements (Gold Medal,

Top Ranks etc.) 0.8031

Infra structure 0.7337

Fees Structure 0.6163

Location of the college 0.6449

Quality of the faculty 0.7541

Research facilities 0.6408

Placement facilities 0.8245

Placement track record 0.7898

Extra-curricular activities 0.6153

Co-curricular activities 0.6051

Transport facilities 0.7306

Hostel facilities 0.6561

Personal safety of the student 0.7061

The positive ideal solution and the negative ideal

solution obtained from the weighted normalized decision

matrix are as follows:

POSITIVE IDEAL SOLUTION = {0.0690, 0.0877,

0.0893, 0.0392, 0.0926, 0.0741, 0.0800, 0.0755, 0.0800,

0.0755, 0.0755, 0.0909, 0.0769, 0.0755}

NEGATIVE IDEAL SOLUTION = {0.0345, 0.0351,

0.0536, 0.0784, 0.0370, 0.0556, 0.0400, 0.0377, 0.0200,

0.0377, 0.0377, 0.0364, 0.0192, 0.0566}

Table 4. PIS and NIS, Relative Closeness Coefficient and ranking for Adaptive TOPSIS

Alternatives

Distance

( )

Distance

( )

RCC

( ) Rank

A1 0.0702 0.0688 7

A2 0.0593 0.0707 6

A3 0.0845 0.0458 16

A4 0.0709 0.0546 10

A5 0.0801 0.0515 13

A6 0.0546 0.0752 5

A7 0.0421 0.0983 2

A8 0.0242 0.1131 1

A9 0.0405 0.0904 4

A10 0.0775 0.0464 14

A11 0.0743 0.0520 11

A12 0.0760 0.0532 12

A13 0.0673 0.0561 9

A14 0.0703 0.0611 8

A15 0.0808 0.0476 15

A16 0.0906 0.0369 17

A17 0.0401 0.0935 3

The PIS and NIS is based on the benefit and cost

criteria. In PIS, the benefit criteria should be maximized

and cost criteria should be minimized and in NIS the

benefit criteria should be minimized and cost criteria

should be maximized. The PIS and NIS helps to calculate

the distance. The Adaptive TOPSIS method ranked the

first college as A8: Pondicherry University, Pondicherry.

This college is ranked first, because the relative closeness

coefficient value is greater when compared with other

college. The distance of the alternative to PIS & NIS, the

relative Closeness coefficients and the ranking for

Adaptive TOPSIS is shown in Table 4.

In the same way, the original decision matrix and

weights from the Table 2 and Table 3 is applied in

COPRAS method. The COPRAS method also ranked the

first college as A8: Pondicherry University, Pondicherry.

This college is ranked first, because the utility degree

value is 100% when compared with other college. Table 5

shows the Utility degree and ranking order of the college.

Table 5. Utility degree and ranking of an alternative using COPRAS

Alternative Utility degree ( ) Rank

A1 8

A2 6

A3 16

A4 10

A5 13

A6 5

A7 2

A8 1

A9 4

A10 12

A11 14

A12 11

A13 9

A14 7

A15 15

A16 17

A17 3

On comparing the result from Adaptive TOPSIS and

COPRAS method both Adaptive TOPSIS and COPRAS

method ranks Pondicherry University as a best college. In

this research, the MCDM methods are implemented in

MATLAB version7.9.0.529 (R2009b). The collected data

has been processed in MATLAB.

VI. RESULTS AND DISCUSSION

By comparing the Multi Criteria Decision making

methodology, COPRAS with the proposed methodology

Adaptive TOPSIS the following results are obtained. Two

methods Adaptive TOPSIS and COPRAS are

implemented with the same input to obtain the best and the

worst alternative. The ranking of Adaptive TOPSIS and

COPRAS method are compared by the parameters. Each



parameter is applied in both the method in order to find

the better method. The efficiency of algorithm is

determined by the following two metrics.

a) Computation time of the algorithm (Time

Complexity)

b) Space required by the algorithm (Space

Complexity)

Table 6. Time and Space Complexity in S-TOPSIS and COPRAS

Methods Time complexity

(seconds)

Space complexity

(bytes)

Adaptive

TOPSIS 0.005072 6656

COPRAS 0.025635 6992

Table 6 describes the Time and Space Complexity of

Adaptive TOPSIS and COPRAS. From the results it is

observed that the Adaptive TOPSIS has taken limited

computation time and space complexity.

Fig.2. Time Complexity of Adaptive TOPSIS and COPRAS

Fig.3. Space Complexity of Adaptive TOPSIS and COPRAS

Figure 2 shows diagrammatical view of Adaptive

TOPSIS which has less time complexity. Where, figure 3

shows diagrammatical view of Adaptive TOPSIS which

has less space complexity than COPRAS method.

A. Sensitivity An alysis

Sensitivity analysis measures the impact on the

outcome by changing one or more key input values.

Sensitivity analysis is used to investigate how sensitive

the ranking of alternatives when changes in weights and

belief degrees for certain attributes [18]. Hence,

performing a Sensitivity Analysis on the results of a

decision problem may provide valuable information to the

decision maker about the robustness of the solution. The

sensitivity analysis is conducted in different way by using

weight. Generally, the total sum of the weight is always

equal to one. That is the range of weight is from 0.1 to 0.9.

The Sensitivity analysis is conducted in Adaptive

TOPSIS and COPRAS method to check robustness of the

solution in these methods. Sensitivity analysis can be

performed by changing weights in different method. The

weights are change in two different methods and the

efficiency is checked.

Assign all attributes a weight value of 1, called

basic weight.

Sensitivity analysis on exchanging each criterions

weight with another criterions weight [19].

The Adaptive TOPSIS and COPRAS method are

performed by changing all the weights of the criteria to 1.

The result of sensitivity analysis is shown in below table

when all the weights have changed to 1. From the Table 7

it has shown that the rank for the alternatives is changing

in Adaptive TOPSIS when conducting Sensitivity

analysis. The alternatives are A5 – A7 – A10 – A17.

In the same way, Sensitivity Analysis is conducted in

COPRAS method. The rank of the following alternative is

getting changed in this method. The alternatives are A1 –

A11 – A13 – A15. On seeing the result of sensitivity

analysis, the ranking of both methods are changing

equally when all the criteria’s weights are changed to 1.

Figures 4 and Figure 5 have clearly shown that the rank

of both Adaptive TOPSIS and COPRAS are changing

equally when weights are change to 1.

Then the Sensitivity analysis on exchange each

criterions weight with another criterion weight is

conducted. Table 8 shows the result of sensitivity analysis

on exchanging weights. From the Table 8 the rank for the

following alternatives is changed in Adaptive TOPSIS

when conducting Sensitivity analysis. The alternatives are

A5 – A7 – A9 – A10 – A17. In the same way, Sensitivity

Analysis is conducted in COPRAS method.

The rank of the following alternative is getting changed

in this method. The alternatives are A1 – A5 – A11 – A13

– A16. On seeing the result of sensitivity analysis, the

ranking of both methods are changing equally when all

the criteria’s weights are exchanged. But the best

alternative in both the method doesn’t get changed. The

Sensitivity Analysis is conducted in two different ways

where both the method the ranking result from both

Adaptive TOPSIS and COPRAS method are changing

equally.

0

0.005

0.01

0.015

0.02

0.025

0.03

AdaptiveTOPSIS

COPRAS

Tim

e (

in s

eco

nd

s)

MCDM Methods

TimeComplexity

6400

6500

6600

6700

6800

6900

7000

AdaptiveTOPSIS

COPRAS

Spac

e (

byt

es)

MCDM Methods

Space Complexity



Table.7. Sensitivity analysis in Adaptive TOPSIS and COPRAS when all the weights are 1

Alternatives Adaptive TOPSIS COPRAS

Before After Before After

RCC RANK RCC RANK RCC RANK RCC RANK

A1 0.4950 7 0.5046 7 70.11% 8 70.06% 9

A2 0.5439 6 0.5284 6 75.46% 6 74.96% 6

A3 0.3510 16 0.3539 16 63.24% 16 63.53% 16

A4 0.4352 10 0.4323 10 68.42% 10 68.39% 10

A5 0.3911 13 0.3897 14 65.18% 13 65.14% 13

A6 0.5793 5 0.5788 5 78.17% 5 78.31% 5

A7 0.7003 2 0.6834 3 91.87% 2 91.73% 2

A8 0.8239 1 0.8006 1 100% 1 100% 1

A9 0.6908 4 0.6765 4 83.89% 4 82.33% 4

A10 0.3747 14 0.3932 13 66.08% 12 66.71% 12

A11 0.4117 11 0.4242 11 65.08% 14 64.96% 15

A12 0.4115 12 0.4111 12 66.85% 11 66.98% 11

A13 0.4545 9 0.4563 9 70.04% 9 70.18% 8

A14 0.4648 8 0.4765 8 71.32% 7 71.64% 7

A15 0.3708 15 0.3685 15 64.89% 15 65.06% 14

A16 0.2896 17 0.2931 17 61.33% 17 61.45% 17

A17 0.7000 3 0.6871 2 87.05% 3 86.60% 3

Fig.4. Sensitivity Analysis on changing weights to 1 for Adaptive TOPSIS

In Adaptive TOPSIS, 4 ranks are getting changed when

Sensitivity analysis is conducted by changing all the

weights to 1. And 5 ranks are getting changed when

Sensitivity Analysis is conducted on exchanging weights.

In the same way, for COPRAS method, 4 ranks are

getting changed when Sensitivity analysis is conducted by

Fig.5. Sensitivity Analysis on changing weights to 1 for COPRAS

changing all the weights to 1. And 5 ranks are getting

changed when Sensitivity Analysis is conducted on

exchanging weights. But the best alternative doesn’t get

changed in both the method. Both the result shows that

the proposed method Adaptive TOPSIS is efficient and

compared method COPRAS also efficient when this

parameter is applied.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Weig

hts

Alternatives

Sensitivity Analysis (Adaptive TOPSIS)

1

2

3

4

5

6

7

8

9

10

11

12

13

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15

16

17

1 3 5 7 9 11 13 15 17

Weig

hts

Alternatives

Sensitivity Analysis (COPRAS)



Table 8. Sensitivity analysis in Adaptive TOPSIS and COPRAS when the weights are exchanged

Alternatives

Adaptive TOPSIS COPRAS



A1 0.4950 7 0.5046 7 70.11% 8 70.06% 9

A2 0.5439 6 0.5284 6 75.46% 6 74.96% 6

A3 0.3510 16 0.3539 16 63.24% 16 63.53% 16

A4 0.4352 10 0.4323 10 68.42% 10 68.39% 10

A5 0.3911 13 0.3897 14 65.18% 13 65.14% 13

A6 0.5793 5 0.5788 5 78.17% 5 78.31% 5

A7 0.7003 2 0.6834 3 91.87% 2 91.73% 2

A8 0.8239 1 0.8006 1 100% 1 100% 1

A9 0.6908 4 0.6765 4 83.89% 4 82.33% 4

A10 0.3747 14 0.3932 13 66.08% 12 66.71% 12

A11 0.4117 11 0.4242 11 65.08% 14 64.96% 15

A12 0.4115 12 0.4111 12 66.85% 11 66.98% 11

A13 0.4545 9 0.4563 9 70.04% 9 70.18% 8

A14 0.4648 8 0.4765 8 71.32% 7 71.64% 7

A15 0.3708 15 0.3685 15 64.89% 15 65.06% 14

A16 0.2896 17 0.2931 17 61.33% 17 61.45% 17

A17 0.7000 3 0.6871 2 87.05% 3 86.60% 3

Fig.6. Sensitivity Analysis on Exchanging weights for Adaptive

TOPSIS

Fig.7. Sensitivity Analysis on Exchanging weights for COPRAS

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12

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15

16

17

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Weig

hts

Alternatives

Sensitivity Analysis on Exchanging

weights for Adaptive TOPSIS

1

2

34

5

6

7

8

9

10

11

12

13

14

15

16

171 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

We

igh

ts

Alternatives

Sensitivity Analysis on Exchanging weights for COPRAS



B. Rank Reversal

Rank reversal means that the ranking between two

alternatives might be reversed after some variation occurs

to the decision problem, like adding a new alternative,

dropping an old alternative or replacing a non-optimal

alternative by a worse one etc. Usually such a rank

reversal is undesirable for decision-making problems. If a

method does allow it to happen, the validity of the

method could be questioned. Rank reversal of adding and

removing the alternatives are taken for evaluation [20].

And they are applied in Adaptive TOPSIS and COPRAS

method to check the efficiency.

The new alternative 18 is introduced in the original

data. The Relative Closeness Coefficient and ranks obtain

before and after rank reversal is shown in the below Table

9. On conducting the Rank Reversal for Adaptive

TOPSIS and COPRAS the best rank in both the method

doesn’t get changed on adding a new alternative. The

Table 9 has shown that the rank reversal issues in both the

method are limited and no changes in the best alternative

even the new alternative is added.

Figure 8 and Figure 9 have clearly shown that the best

alternative doesn’t get change. The rank remains same for

the following alternative A7 - A8 - A12 - A17 in

Adaptive TOPSIS. Then for COPRAS method the rank

remains same for A7 – A8.

Table 9. Rank Reversal in Adaptive TOPSIS and COPRAS for adding a new Alternative

Alternativ

es




A1 0.4950 7 0.5046 7 70.11% 8 70.06% 9

A2 0.5439 6 0.5284 6 75.46% 6 74.96% 6

A3 0.3510 16 0.3539 16 63.24% 16 63.53% 16

A4 0.4352 10 0.4323 10 68.42% 10 68.39% 10

A5 0.3911 13 0.3897 14 65.18% 13 65.14% 13

A6 0.5793 5 0.5788 5 78.17% 5 78.31% 5

A7 0.7003 2 0.6834 3 91.87% 2 91.73% 2

A8 0.8239 1 0.8006 1 100% 1 100% 1

A9 0.6908 4 0.6765 4 83.89% 4 82.33% 4

A10 0.3747 14 0.3932 13 66.08% 12 66.71% 12

A11 0.4117 11 0.4242 11 65.08% 14 64.96% 15

A12 0.4115 12 0.4111 12 66.85% 11 66.98% 11

A13 0.4545 9 0.4563 9 70.04% 9 70.18% 8

A14 0.4648 8 0.4765 8 71.32% 7 71.64% 7

A15 0.3708 15 0.3685 15 64.89% 15 65.06% 14

A16 0.2896 17 0.2931 17 61.33% 17 61.45% 17

A17 0.7000 3 0.6871 2 87.05% 3 86.60% 3

A18

(new)

Table 10. Rank Reversal in Adaptive TOPSIS and COPRAS for removing the worst Alternative

Alternatives




A1 0.4950 7 0.4724 7 70.11% 8 70.06% 9

A2 0.5439 6 0.5284 6 75.46% 6 74.96% 6

A3 0.3510 16 0.3539 16 63.24% 16 63.53% 16

A4 0.4352 10 0.4323 10 68.42% 10 68.39% 10

A5 0.3911 13 0.3897 14 65.18% 13 65.14% 13

A6 0.5793 5 0.5788 5 78.17% 5 78.31% 5

A7 0.7003 2 0.6834 3 91.87% 2 91.73% 2

A8 0.8239 1 0.8006 1 100% 1 100% 1

A9 0.6908 4 0.6765 4 83.89% 4 82.33% 4

A10 0.3747 14 0.3932 13 66.08% 12 66.71% 12

A11 0.4117 11 0.4242 11 65.08% 14 64.96% 15

A12 0.4115 12 0.4111 12 66.85% 11 66.98% 11

A13 0.4545 9 0.4563 9 70.04% 9 70.18% 8

A14 0.4648 8 0.4765 8 71.32% 7 71.64% 7

A15 0.3708 15 0.3685 15 64.89% 15 65.06% 14

A16 0.2896 17 0.2931 17 61.33% 17 61.45% 17

A17 0.70000 3 0.6871 2 87.05% 3 86.60% 3



Fig.8. Rank Reversal for adding alternative in Adaptive TOPSIS

Fig.9. Rank Reversal for adding alternative in COPRAS

Fig.10. Rank Reversal on removing an alternative in Adaptive TOPSIS

Fig.11. Rank Reversal on removing an alternative in COPRAS

On conducting the Rank Reversal for Adaptive

TOPSIS and COPRAS the best rank in both the method

doesn’t get changed on removing the worst alternative.

Table 10 has shows the result of Adaptive TOPSIS and

COPRAS method before and after removing the

alternative. The rank remains same for the following

alternative A1 - A2 - A3 - A6 - A7 – A8 – A9 – A12 –

A13 – A14 – A15 – A17 in Adaptive TOPSIS. And for

COPRAS method all ranks remains same. The above

Figure 10 and Figure 11 show the rank reversal on

removing the alternative.

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12

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16

17

181 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

We

igh

ts

Alternatives

Rank Reversal for adding alternative in Adaptive TOPSIS

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18

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Weig

hts

Alternatives

Rank Reversal for adding alternative in

COPRAS

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16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Weig

hts

Alternatives

Rank Reversal on removing an

alternative in Adaptive TOPSIS

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Weig

hts

Alternatives

Rank Reversal on removing an

alternative in COPRAS



C. Evaluation of Adaptive TOPSIS

The Adaptive TOPSIS is evaluated using the following

parameters: Time and Space Complexity, Sensitivity

analysis and Rank Reversal. The result obtain from Time

and Space complexity from Table 6 shows that both

complexity are less in Adaptive TOPSIS on comparing

with COPRAS method. The time complexity in Adaptive

TOPSIS is 0.005072 seconds and the space complexity is

6656 bytes. Then the sensitivity analysis is conducted in

two different methods. The weights for all the criteria are

changed to 1 and the weights for all the criteria’s are

exchanged with each other. Both the methods of

sensitivity analysis are applied in Adaptive TOPSIS and

COPRAS method. The result from sensitivity analysis is

shown in Table 7 and Table 8. The Figure 4 and Figure 5

show the pictorial representation of the result on

conducting sensitivity analysis by changing all the

weights to 1. And Figure 6 and Figure 7 show the result

of sensitivity analysis on exchanging weights. The result

on conducting sensitivity analysis shows that the

proposed method Adaptive TOPSIS and COPRAS

method performs equally. Both the result shows that the

proposed method Adaptive TOPSIS is efficient.

Finally, Rank Reversal is conducted in Adaptive

TOPSIS and COPRAS method. The rank reversal is

conducted by adding and removing the alternative. The

Rank reversal results are shown in Table 9 and Table 10.

According to the result of Adaptive TOPSIS

method, A 8 is the best among the 17 alternatives. Since

the ranking is slightly different from the rank obtain

before ranking reversal. It is no wonder that different

methods may produce slightly different rankings. The

best alternative A8 is not getting changed. Then the worst

alternative A 1 6 is dropped out of the original alternative

set which is shown in Table 10. The best alternative A8

remains same. The rank in Adaptive TOPSIS and

COPRAS method are doesn’t get reversed when an

alternative is added or removed.

VII. CONCLUSION

Multi Criteria Decision Making is widely used for

decision making problem where there are several factors

in obtaining the best solution and different methods are

used for solving complex problem. The problem is to rank

the engineering college in Cuddalore and Puducherry.

Many algorithms are available in MCDM where TOPSIS

is one of the most preferred on when compared to other

methods. The proposed work introduces a new MCDM

approach which Simplifies TOPSIS method. The

performance of the proposed method, Adaptive TOPSIS

is compared with COPRAS method. The efficiency of

algorithms is measured in terms of Time and space

complexity, Sensitivity Analysis and Rank Reversal. The

Proposed method, Adaptive TOPSIS attains a better result

with time and space complexity, Sensitivity Analysis and

Rank Reversal. As a result of the comparative analysis on

Adaptive TOPSIS with COPRAS method, the proposed

method attains better result. In future, Adaptive TOPSIS

method can be compared with other Multi Criteria

Decision Making methods. The efficiency of the

algorithms can be evaluated with other parameters.

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Authors’ Profiles

Travis Miranda Lakshmi is working toward

the Ph.D. degree in computer science with

Bharathiar University, Coimbatore, India. She

is an Assistant Professor with the PG and

Research Department of Computer Science, St.

Joseph’s College (Autonomous), Cuddalore,

India. Her research interests include

multicriteria decision making, business intelligence and

software engineering.

Venkatasamy Prasanna Venkatesan received

the B.Sc. degree in physics from Madras

University, Chennai, India, in 1986, the M.C.A

degree from Pondicherry University,

Puducherry, India, in 1990, and the M.Tech.

and Ph.D. degrees from Pondicherry University,

both in computer science and engineering, in

1995 and 2008, respectively. He is an Associate Professor of

Banking Technology with Pondicherry University, Puducherry,

India. He has over 20 years of teaching and research experience

in the field of computer science and engineering and banking

technology. He has developed an architectural reference model

for multilingual software. His research interests include

software engineering, service oriented architecture, pervasive

computing, bankruptcy prediction methods, and business

intelligence.

Aruldoss Martin received the B.Sc. degree

in chemistry from St. Joseph’s College,

Cuddalore, India, in 1997, the M.C.A. degree

from Bharathidasan University, Trichy, India,

in 2000, the M.E. degree in computer science

and engineering from Mailam Engineering

College, Mailam, India, in 2007, and the

Ph.D. degree in computer science and engineering (banking

technology) from Pondicherry University, Puducherry, India, in

2014. He is an Associate Professor with the Department of

Master of Computer Applications, Sri Manakula Vinayagar

Engineering College, Puducherry, India. He also is a Research

Scholar of Banking Technology, Pondicherry University,

Puducherry, India. His research interests include business

intelligence, bankruptcy prediction

How to cite this paper: T. Miranda Lakshmi, V. Prasanna Venkatesan, A. Martin,"An Identification of Better

Engineering College with Conflicting Criteria using Adaptive TOPSIS", International Journal of Modern Education and

Computer Science(IJMECS), Vol.8, No.5, pp.19-31, 2016.DOI: 10.5815/ijmecs.2016.05.03

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